2024 Hoeffding's inequality

Hoeffding's inequality

Author: uipm

August undefined, 2024

NettetHoeffding's lemma: Suppose x is an random variable, x∈ [a, b] , and E (x)=0 , then for any t>0 , the following inequality holds： E (e^ {tx})\leq exp\frac {t^2 (b-a)^2} {8} We prove the lemma first: Obviously, f (x)=e^ {tx} is a convex function, so for any α∈ [0,1] , we have: f (αx_1+ (1-α)x_2)\le αf (x_1)+ (1-α)f (x_2) Nettet13. apr. 2024 · I've read in a paper using Hoeffding's inequality to derive a bound on the probability of the difference of means of two samples being larger than a threshold that "Hoeffding's bound greatly overestimates the probability of large deviations for distributions of small variance; in fact, it is equivalent to assuming always the worst …

machine learning - Hoeffding

Nettet1. apr. 2024 · Hoeffding’s inequality (Hoeffding, 1963) has been applied in a variety of scenarios, including random algorithm analysis (Dubhashi and Panconesi, 2012), statistical learning theory (Fan et al., 2024), and information theory (Raginsky and Sason, 2013) etc. NettetBased on Hoeffding's theorem, one could easily find the minimum number of samples required for the inequality $\Pr \left( \bar{X} - \mathrm{E} [\bar{X}] ... However, this paper from Microsoft Research states that Hoeffding's inequality "originally targets sampling … korean seasoned raw beef

Is Hoeffding

Nettet这两天也关注集中不等式（Concentration inequality），书籍没找到（也没有去找），仅搜了一些资料理解了一下概念。. 先来看Wikipedia中词条 Concentration inequality 中的描述：. In probability theory, concentration inequalities provide bounds on how a random variable deviates from some value ... NettetAzuma's inequality. In probability theory, the Azuma–Hoeffding inequality (named after Kazuoki Azuma and Wassily Hoeffding) gives a concentration result for the values of martingales that have bounded differences. Suppose is a martingale (or super-martingale) and. almost surely. Then for all positive integers N and all positive reals , If X ... Nettet20. sep. 2024 · What the Hoeffding Inequality gives us is a probabilistic guarantee that v doesn’t stray too far from 𝜇. eps is some small value which we use to measure the deviation of v from 𝜇. We claim that the probability of v being more than eps away from 𝜇 is less … mangrove mountain ashram

An improved Hoeffding’s inequality for sum of …

arXiv:math/0410159v1 [math.PR] 6 Oct 2004

Nettet24. okt. 2024 · Hoeffding's inequality was proven by Wassily Hoeffding in 1963. Hoeffding's inequality is a special case of the Azuma–Hoeffding inequality and McDiarmid's inequality. It is similar to the Chernoff bound, but tends to be less sharp, … Nettet3. feb. 2024 · 在概率论中，霍夫丁不等式给出了随机变量的和与其期望值偏差的概率上限，该不等式被Wassily Hoeffding于1963年提出并证明。霍夫丁不等式是Azuma-Hoeffding不等式的特例，它比Sergei Bernstein于1923年证明的Bernstein不等式更具一般性。这几个不等式都是McDiarmid不等式的特例。 2.霍夫丁不等式 2.1.伯努利随机变量 … mangrove monitor species mixed tankNettetTheorem 1 Hoeﬀding’s Inequality Let Z 1,Z 2,...,Zn be independent bounded random variables such that Z i ∈ [a i,b i] with probability 1. Let S n = P n i=1 Z i. Then for any t > 0, we have P( S n −E[S n] ≥ t) ≤ 2e − 2t 2 P n i=1 (bi−ai)2 Proof: The key to proving … korean seasoned small crab

"Nettet15. jan. 2002 · Hoeffding's inequality is a key tool in the analysis of many problems arising in both probability and statistics. Given a sequence Y ≡ (Y i: i⩾0) of independent and bounded random variables, Hoeffding's inequality provides an exponential bound … " - Hoeffding's inequality

Hoeffding's inequality

NettetVershynin’s book [14] gives general Hoeffding and Bernstein-type inequalities for sums of indepen-dent sub-Gaussian or sub-exponential random variables. In situations where the bounded difference inequality is used, one would like to have analogous bounds for general functions. In this work we NettetIn probability theory, Hoeffding's inequality provides an upper bound on the probability that the sum of bounded independent random variables deviates from its expected value by more than a certain amount. Hoeffding's inequality was …

Did you know?

http://cs229.stanford.edu/extra-notes/hoeffding.pdf Nettet28. apr. 2024 · We investigate Hoeffding’s inequality for both discrete-time Markov chains and continuous-time Markov processes on a general state space. Our results relax the usual aperiodicity restriction in the literature, and the explicit upper bounds in the …

NettetSimilar results for Bernstein and Bennet inequalities are available. 3 Bennet Inequality In Bennet inequality, we assume that the variable is upper bounded, and want to estimate its moment generating function using variance information. Lemma 3.1. If X EX 1, then 8 0: lnEe (X ) (e 1)Var(X): where = EX Proof. It sufﬁces to prove the lemma when ... Nettet27. jul. 2012 · VC Theory: Hoeffding Inequality. 之前提过的 Professor Yaser Abu-Mostafa 的机器学习课程在 Lecture 5、6、7 三课中讲到了 VC Theory 的一些内容，用来回答他在课程中提到的“Can We Learn？. ”这个问题。. 更具体地来说，他这里主要解决了 binary classification 问题中的 Learnability 的问题 ...

In probability theory, Hoeffding's inequality provides an upper bound on the probability that the sum of bounded independent random variables deviates from its expected value by more than a certain amount. Hoeffding's inequality was proven by Wassily Hoeffding in 1963. Hoeffding's inequality is a … Se mer Let X1, ..., Xn be independent random variables such that $${\displaystyle a_{i}\leq X_{i}\leq b_{i}}$$ almost surely. Consider the sum of these random variables, $${\displaystyle S_{n}=X_{1}+\cdots +X_{n}.}$$ Se mer The proof of Hoeffding's inequality follows similarly to concentration inequalities like Chernoff bounds. The main difference is the use of Se mer • Concentration inequality – a summary of tail-bounds on random variables. • Hoeffding's lemma Se mer The proof of Hoeffding's inequality can be generalized to any sub-Gaussian distribution. In fact, the main lemma used in the proof, Hoeffding's lemma, implies that bounded random variables are sub-Gaussian. A random variable X is called sub-Gaussian, if Se mer Confidence intervals Hoeffding's inequality can be used to derive confidence intervals. We consider a coin that shows heads with probability p and tails with probability 1 − p. We toss the coin n times, generating n samples Se mer NettetThe right hand side would then be the dirac mass at 0 (as seen in the proof of Hoeffding's inequality). There can't be any other example as that would contradict the hypothesis that $\bar{X}$ is bounded, since

Nettet霍夫丁不等式（英語：Hoeffding's inequality）適用於有界的隨機變數。設有兩兩獨立的一系列隨機變數X1,…,Xn{\displaystyle X_{1},\dots ,X_{n}\!}。 P(Xi∈[ai,bi])=1.{\displaystyle \mathbb {P} (X_{i}\in [a_{i},b_{i}])=1.\!} 那麼這n個隨機變數的經驗期望： …

NettetUpper bounds are derived for the probability that the sum S of n independent random variables exceeds its mean ES by a positive number nt. It is assumed that the range of each summand of S is bounded or bounded above. The bounds for Pr S — ES ≥ nt depend only on the endpoints of the ranges of the summands and the mean, or the … mangrove mountain country fairNettet10. mai 2024 · The arguments used to prove the usual (1D) Hoeffding's inequality don't directly extend to the random matrices case. The full proof of this result is given in Section 7 of Joel Tropp's paper User-friendly tail bounds for sums of random matrices, and relies mainly on these three results : mangrove mountain pharmacyNettetHoeffding's inequality was proven by Wassily Hoeffding in 1963. Hoeffding's inequality is a special case of the Azuma–Hoeffding inequality and McDiarmid's inequality. It is similar to the Chernoff bound, but tends to be less sharp, in particular when the variance of the … mangrove mountain windNettet24. apr. 2024 · To develop an optimal concentration inequality to replace Hoeffding’s inequality in UCB algo-rithms it is therefore legitimate that we ask the same question that Hoeffding’s inequality answers: for a speciﬁc possible mean of the data distribution, what is the maximum probability of receiving the relevant sample statistics? korean s curlNettet23. jan. 2024 · The inequality I'm having trouble with is the following : The first line is clearly true by the law of total expectation, and I understand that the second line is a direct application of Hoeffding's inequality since, conditional on the data, is a sum of i.i.d … mangrove mountain greek orthodox churchhttp://chihaozhang.com/teaching/SP2024spring/notes/lec8.pdf mangrove mountain golf clubNettet11. feb. 2024 · Download a PDF of the paper titled Some Hoeffding- and Bernstein-type Concentration Inequalities, by Andreas Maurer and Massimiliano Pontil Download PDF Abstract: We prove concentration inequalities for functions of independent random … mangrove mountain weather bom